You'll gain access to interventions, extensions, task implementation guides, and more for this lesson.

Big Ideas:
The graph of f(x)=(a+bx)/x has a characteristic shape.
When a and x are positive, f(x) is decreasingly decreasing, and the graph is a curve.
The graph of f(x) has a horizontal asymptote at y=b.
In this task, students create and graph a rational function that relates the number of people attending an end of the year trip, to the cost per person of the trip. This task builds on task 5 by introducing an additional parameter: in addition to the cost of the bus, each student must also contribute $20 for gas. This creates a rational function of the form f(x)=(a+bx)/x. Students use the graph to explore key features of the graph, including its maximum, whether it is increasing or decreasing, and its infinite behavior.
Vocabulary: graph, plot, point, function, asymptote
Special Materials:
Graph paper